Ship defensive power calculations

[giantsquid]

Reading again the good and old Harpoon II Strategy Guide for PC and the book Fleet Tactics, I found some interesting consideration to calculate ship defensive power, or their ability to shoot down enemy planes or missiles in a single salvo with the ship SAM system.

The formula is: #radars x Prob kill x #engagements, where
Number of radars/firing channel of the SAM system (1-10+)
Prob. Kill (0.1-0.9 for 1 or 2 missiles on each target) of the SAM system against the target
Numbers of consecutive engagement possible after the attackers are discovered and before they enter inside the minimum range (1 for point defence, 3 for area defence against high flying targets, but can actually vary a lot if weapons are supersonic or sea skimmers)

Example: Udaloy SA-N-9 vs Harpoon in the late eighties
4 x 0,7 (firing two missiles) x 1 = 2,8
That is the likely number of missiles that will be probably shot down in an attack. So to have a decent possibility to survive the russian SAMs at least 4 Harpoons must be fired to the Udaloy, without taking in considerations CIWS and degradation by ECM.
Another Harpoon can be added for CIWS. The final Ph (Prob. Hit) of the surviving Harpoons will be about 0,5 and not 0,9, because of chaff, jammers and possible malfunctions and I probably need two impacting Harpoons to sink a ship like Udaloy.
About 3 are taken by SAMs, 1 by CIWS = 4 hard kills
Ph is 0,5 so i need at least 4 missiles to have 2 good impacts (about 0,8 prob to have at least 2 hits).
So the final good estimate could be 8 Harpoons to kill the Udaloy.

I think this system can be a good guide to allocate weapons on alerted targets. What do you think?

[Tailhook]

If you go into the database for ships and ground units, you'll see the "Missile Defense: X Harpoon / SLAM / Maverick equivalents" statistic. I don't recall the specific factors, but I do know that it accounts for damage points (DPs), armor, and defensive systems such as SAMs, chaff, etc.

Using your scenario of a late 80s Udaloy I (1988 to be specific) we have a defense value of 16 Harpoons. To test this, I sent 4x A-6E TRAM aircraft with 4x harpoons each. The Udaloy was emitting fully as well as using OECM jammers. In the first test not a single harpoon got through. In a second run only a single missile got through (well 2 did but 1 malfunctioned) for about 33% of it's health. This missile destroyed the aviation facilities but did not damage any of the sensors or defensive systems. I suspect if it had then the last 4 missiles still airborne would have finished. But that's the random nature of the test. So as you can see from a fully alerted ship, the recommended by the game 16 isn't enough (note that they had no jammers either) and your 8 definitely would not have been.

Repeated the test with an Udaloy with full emissions control. Attacking force was once again 4 A-6E TRAM with 4x harpoons. The Intruders went in with radars off to avoid alerting (simulating a realistic attack) with a P-3 at range in another direction for radar spotting. The Udaloy was not aware of the threat until the Harpoon seekers went active, at which point it energized all radars and OECM jammers, detecting the target at ~5 nm. Of the 16 missiles, 3 made it through the weapons with 1 being decoyed and the other 2 hitting the ship, causing fire and floods and reducing speed. It took about 40 minutes to suppress the fire and floods, and the ship limped away at 12 knots.

I did not run the second scenario again but I suspect that without ARM or jamming, you have about a 50% chance of sinking the Udaloy in this scenario using the games recommended 16 missiles. I would guess that an alert ship able to engage at maximum SA-N-9 range would have a 75% chance of survival against 16 missiles. Therefore I think your calculations are too low.

[magi]

interesting....

[giantsquid]

Thanks Tailhook for your excellent examples.
I didn't run any test so far.

I think the missile defense should take in consideration only hard kill systems but I wait the devs for this… Anyway it’s a general indication and not always reliable.
For example a value of 6 is given to Type-42 UK DDG against Harpoon in the first eighties but they cannot intercept missiles flying so low

My updated calculation for Udaloy could be:
4 x 0,9 (firing two missiles, higher Pk) x 2 (more engagements) = 6,4
CIWS – 2 missiles

More is probably too much at that time. Each SA-N-9 radar should be able to engage two target, I think, but I cannot find confirm on the charts.

[mikmykWS]

Check out Wayne Hughes's Fleet Tactics and Coastal Combat. Chapter 11 discusses some Missile salvo equations but the whole book is valuable in terms of thinking about and developing strategies for the sim.

Mike

[giantsquid]

Thanks Mike, that's the book that kicked my interest
I will keep on with testing. Thanks again Tailhook

Francesco